Question

Simplify :
${\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-5}$
[2 marks]

Answer 1

${\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-5}=\frac{5^{-7}\times 8^{-5}}{8^{-7}\times 5^{-5}}=\frac{8^{+7}\times 8^{-5}}{5^{-5}\times 5^{+7}}\left[1\mathrm{mark}\right]\mathrm{Now},\mathrm{by}\mathrm{using}\mathrm{laws}\mathrm{of}\mathrm{exponent}{a}^m\times a^n=a^{m+n}\Rightarrow \frac{8^{+7}\times 8^{-5}}{5^{-5}\times 5^{+7}}=\frac{8^{+7-5}}{5^{+7-5}}=\frac{8^2}{5^2}=\frac{64}{25}\left[1\mathrm{mark}\right]$